Question

Use the​ price-demand equation p plus 0.005 x equals 46​, 0 less than or equals p less than or equals 46. Find the elasticity of demand when pequals​$22. If the ​$22 price is decreased by 12​%, what is the approximate percentage change in​ demand?

Answer 1

Answer:

a. -0.92

b. 11% increase in demanded

Explanation:

Given p + 0.005x = 46, 0 ≤ p ≤ 46

Rewriting the demand equation by solving for x as follow:

0.005x = 46 - p

x = (46 - p) / 0.005

x = (46 / 0.005) - (1/0.005)p

x = 9,200 - 200p .................................................................... (1)

Differentiating equation (1) with respect to p, we have:

dx/dp = -200

We can now answer the two questions as follows:

a. Find the elasticity of demand when pequals$22.

To calculate elasticity of demand, the formula for calculating the elasticity of demand is used as follows:

E = Elasticity of demand = (p / x) * (dx / dp) ................... (2)

Since p = $22, we find x in equation (1) by substituting for p as follows:

x = 9,200 - 200 (22) = 4,800

Note that dx/dp = -200

Substituting the values into equation (2), we have:

E = (22 / 4,800) * (-200) = -0.92

Note: Since the absolute value of E i.e. |-0.92| is less than one, the demand is inelastic.

If the ​$22 price is decreased by 12​%, what is the approximate percentage change in​ demand?

To do calculate this, we use the following formula for calculating the elasticity of demand:

E = % change in demand / % change in price ............. (3)

Since,

E = - 0.92

% change in price = -12%, or -0.12

Substituting the values into equation (3) and solve for % change in demand, we have:

-0.92 = % change in demand / -0.12

% change in demand = [-0.12] * [-0.92] = 0.11, or 11%

Therefore, the approximate percentage change in​ demand if the ​$22 price is decreased by 12​% is 11% increase in demand.